GATE CE 2015 Set 2 — Question 53
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Water Resources Engineering → Fluid Properties & Statics → Hydrostatic Forces
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Question
A triangular gate with a base width of 2 m and a height of 1.5 m lies in a vertical plane. The top vertex of the gate is 1.5 m below the surface of a tank which contains oil of specific gravity 0.8. Considering the density of water and acceleration due to gravity to be 1000 and 9.81 respectively, the hydrostatic force (in kN) exerted by the oil on the gate is ___________
Correct answer
29.3 to 29.5
Solution
Step 1: Identify the properties of the fluid and the gate.
Specific gravity of oil = 0.8.
Density of oil () = .
Acceleration due to gravity () = 9.81 .
Base of the triangular gate () = 2 m.
Height of the triangular gate () = 1.5 m.
Area of the gate () = .Step 2: Determine the depth of the centroid () from the free surface.
The top vertex is 1.5 m below the surface. For a vertical triangle with the vertex pointing up, the centroid is located at a distance of from the vertex.
m.Step 3: Calculate the hydrostatic force ().
N.Step 4: Convert the force to kN.
kN.The hydrostatic force is 29.43 kN, which falls within the range 29.3 to 29.5.
Specific gravity of oil = 0.8.
Density of oil () = .
Acceleration due to gravity () = 9.81 .
Base of the triangular gate () = 2 m.
Height of the triangular gate () = 1.5 m.
Area of the gate () = .Step 2: Determine the depth of the centroid () from the free surface.
The top vertex is 1.5 m below the surface. For a vertical triangle with the vertex pointing up, the centroid is located at a distance of from the vertex.
m.Step 3: Calculate the hydrostatic force ().
N.Step 4: Convert the force to kN.
kN.The hydrostatic force is 29.43 kN, which falls within the range 29.3 to 29.5.
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